Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33832 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3280 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,23,28)(20,29,33,40)(21,34,37,43)(22,25,36,27)(24,39,42,31)(26,44,46,35)(30,47,48,41)(32,49,38,45);(18,20,23,33)(19,24,28,42)(21,30,37,48)(22,38,36,32)(25,41,27,47)(26,45,46,49)(29,43,40,34)(31,44,39,35);(15,17);(19,25)(20,30)(21,35)(22,36)(24,40)(27,28)(29,42)(31,32)(33,48)(34,43)(37,44)(38,39)(41,45)(47,49)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26820);